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K-homology and index theory on contact manifolds

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Acta Mathematica

Abstract

This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus.

The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of Atiyah–Singer type to non-elliptic Fredholm operators.

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Authors and Affiliations

  1. Pennsylvania State University, University Park, PA, 16802, U.S.A

    Paul F. Baum

  2. Dartmouth College, 6188 Kemeny Hall, Hanover, NH, 03755, U.S.A

    Erik van Erp

Authors
  1. Paul F. Baum
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  2. Erik van Erp
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Correspondence to Paul F. Baum.

Additional information

With admiration and affection we dedicate this paper to Sir Michael Atiyah on the occasion of his 85th birthday.

Paul Baum thanks Dartmouth College for the generous hospitality provided to him via the Edward Shapiro fund. Erik van Erp thanks Penn State University for a number of productive and enjoyable visits. PFB was partially supported by NSF grant DMS-0701184. EvE was partially supported by NSF grant DMS-1100570.

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Baum, P.F., van Erp, E. K-homology and index theory on contact manifolds. Acta Math 213, 1–48 (2014). https://doi.org/10.1007/s11511-014-0114-5

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  • DOI: https://doi.org/10.1007/s11511-014-0114-5

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